Anti-Self-Dual Conformal Structures in Neutral Signature
Differential Geometry
2010-07-16 v5 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We review the subject of four dimensional anti-self-dual conformal structures with signature (+ + - -). Both local and global questions are discussed. Most of the material is well known in the literature and we present it in a way which underlines the connection with integrable systems. Some of the results - e.g. the Lax pair characterisation of the scalar-flat Kahler condition and a twistor construction of a conformal structure with twisting null Killing vector - are new.
Cite
@article{arxiv.math/0610280,
title = {Anti-Self-Dual Conformal Structures in Neutral Signature},
author = {Maciej Dunajski and Simon West},
journal= {arXiv preprint arXiv:math/0610280},
year = {2010}
}
Comments
48 pages, 1 figure, contribution to the special volume `Recent developments in pseudo-Riemannian Geometry', ESI-Series on Mathematics and Physics. Revised manuscript with added references. A mistake pointed out by Gueo Grantcharov corrected